If interest is compounded semi-annually, which expression represents the account balance in t years?

Question

If interest is compounded semi-annually, which expression
represents the account balance in t years?

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Diễm Thu 6 months 2021-08-18T18:25:27+00:00 1 Answers 0 views 0

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    2021-08-18T18:26:27+00:00

    Answer:

    The equation to represent the account balance in t years

    A\:=\:P\left(1\:+\:\frac{r}{n}\right)^{2t}

    Step-by-step explanation:

    Given the compound interest equation

    A\:=\:P\left(1\:+\:\frac{r}{n}\right)^{nt}

    here

    A represents Accrued Amount (principal + interest)

    P represents Principal Amount

    I represent Interest Amount

    r represents the Annual interest rate

    t represents Time Involved in years

    n represents the number of compounding periods per unit t

    As we are given that the interest is compounded semi-annually

    i.e. n = 2

    so substituting n = 2 in the equation

    A\:=\:P\left(1\:+\:\frac{r}{n}\right)^{nt}

    A\:=\:P\left(1\:+\:\frac{r}{n}\right)^{2t}       ∵ n = 2

    Thus, the equation to represent the account balance in t years

    A\:=\:P\left(1\:+\:\frac{r}{n}\right)^{2t}

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